Friend has mom in Kharkiv – contact / path to help escort out?

In regards to local evacuation it's unlikely that anybody outside of Kharkiv area will be able to help. If she manages to get through the border to any neighbouring western country she will be taken care of. There is no need to set anything up in advance in current chaotic situation as she would be potentially blocking accommodation for multiple other people.

I'm hosting 6 refugees from Ukraine in Gdansk, northern Poland and the situation is that help is organized on social media and volunteers find accommodation for refugees within minutes, up to several hours after a request is raised. During that time they will have a warm place to stay and food to eat, there are absolutely no people left without help. Just an hour ago I've seen an offer from a person able to provide roof for 500(!) people. It is likely that the situation is already more problematic closer to Ukrainian border, so flexibility to travel further west (including Germany, which started organizing similar help recently) is going to help. Transport from the UKR-POL border is also a non-issue - Ukrainians can use trains for free, there are also private buses and cars picking up groups of people and moving them to various destinations. For free.

To Ukrainians in need - just get through the border and we'll handle it for you from there.

There is very little they can do, I am afraid to say. My mother-in-law is currently in Chernigov (Northern Ukraine). I think the situation is similar in Kharkiv. The city is surrounded, bridges and roads are ruined, they are being bombed all over. We are waiting on legitimate 'green corridors' to be established before people can get out. Russians have continued shelling in Mariupol even after agreeing to let civilians out in a cease-fire. At this point they are no better than terrorists.

I know a church in Siret, Romania is helping people get out - but Kharkiv is a LOOONG way from Kharkiv.